Orthographic projection

Orthographic projection is the solution to the biggest problem that a draughtsman has to solve—how to d»aw. with sufficient clarity, a three-dimensional object on a two-dimensional piece of paper The drawing must show quite clearly the detailed outlines of all the faces and these outlines must be fully dimensioned If the object is very simple, this may be achieved with a freehand sketch. A less simple object could be drawn in either isometric or oblique projections, although both these systems have their disadvantages. Circles and curves are difficult to draw in either system and neither shows more than three sides of an object in any one view. Orthographic projection. because of its flexibility in allowing any number of views of the same obiect. has none of these drawbacks.

Orthographic projection has two forms: First angle and Third angle, we shall discuss both. Traditionally. Bntish industry has used 1st angle whilst the United States of Amenca and. more recently, the Continental countries used the 3rd angle system. There is no doubt that British

HORIZONTAL PLANE

VERTICAL PLANE

industry is rapidly changing to the 3rd angle system end. whilst this wiM take some years to complete. 3rd angle will eventually be the national and international standard of orthographic projection.

Fig. 10/1 shows a stepped block suspended between two planes A plane is a perfectly flat surface. In this case one of tho planes is horizontal and the other is vertical. The view looking on the top of the block is drawn directly above the block on the horizontal plane. The view looking on the si<e of the block is drawn directly in line with the block on the vertical plane. If you now take away the stepped block and. imagining that the two planes are hinged, fold back the horizontal piano so that it lines up with the vertical plane, you are left with two drawings of the block One is a view looking on the top of the block and this is directly above another view looking on the side of the block. These two views are called elevations

Fig. 10/1 3rd angle orthographic projection

Fig. 10/1 3rd angle orthographic projection

Fig. 10/1 shows the block in 3rd angle orthographic projection. The same block is drawn in Fig. 10/2 In 1st angle orthographic projection. You still have a vertical and a horizontal plane but they are arranged differently. The block is suspended between the two planes end the view of the top of the block is drawn on the horizontal plane and the view of the side is drawn on the vortical plane. Again, imagining that the planes ere hinged, the horizontal plane is folded down so that the planes are in line. This results in the drawing of the side of the block being directly above the drawing of the top of the block (compare this with the 3rd angle drawings).

The reason why those two systems ere celled 1 st and 3rd angle is shown in Fig. 10/3. If the horizontal plane (H.P.) and the vertical plane (V.P.) intersect as shown, it produces four quadrants. The first quadrant, or first angle, is the top right and the third is the bottom left. If the block is suspended between the V P. end the H P. in the first and third angles you can see how the views are projected onto the two planes.

So far we have obtained only two views of the block, one on the V P. and one on the H P. With a complicated block this may not be enough This problem is easily solved by introducing another plane. In this case it Is a vertical plane and it will show a view of the end of the block and so, to distinguish it from th« other vertical plane, it is called the end vertical plane (E.V.P.). and the original vertical plane is called the front vertical plan« (F.V.P.).

The E V P. is hinged to the F.V.P. and when the views have been projected onto their planes, the three planes are unfolded and three views of the block are shown. Fig. 10/4.

The drawing on the F.V.P. is called the front elevation (F.E.). the drawing on the E.V.P. is called the end elevation (E.E.) and the drawing on the H P. is called the plan All three views are linked togethor: the plan is diroctly above the F.E.; the E.E. is horizontally in line with the F.E.; and the plan and the E.E. can be linked by drawing 45" projection lines This is why orthographic projection is so important; it isn't just because several views of the same object can be drawn, it is bectuse the views are linked together.

HORIZONTAL PLANE tM.R)

1

J'.

ENO VERTICAL PLANE (EVP)

B

*

FRONT VERTICAL PLANE 1F.YR1

Fig. 1Q/4 3rd angle orthographic projection

Fig. 10/4 »bowed three view» of the block drawn in 3rd angle; Fig. 10/5 »hows three views of the same block drawn in 1st angle.

in this case the F.E. is above the plan and to the left of the E.E. (compare this with 3rd angle). Once egain. the E.E. and the plan can be linked by projection lines drawn ttAP.

The system of suspending the block between three planes and projecting views of the block onto these planes is the basic principle of orthographic projection and must be completely understood if one wishes to study this type of projection any further. This is done in Chapter 13.

The following system is somewhat easier to understand and will meet most of the readers needs

Fig 1CV5 1st angle orthography projection

FRONT VERTICAL PLANE IF.V.PI

as

ENO VERTICAL PLANE CEVP)

¡1

«

il 1« H I'

i

i

it

HORIZONTAL PLANE im n

Fig 1CV5 1st angle orthography projection

Fig. 10/6 chows the same shaped block drawn In 3rd angle protection. First draw the view obtained by looking along the arrow marked F.E. This gives you the front elevation. Now look along the errow marked E.E., (which points from the left) and draw what you see to the left of the front elevation This gives you an end elevation. Now look along the arrow marked E.E., (which points from the right) and draw what you see to the right of the front elevation. This gives you another end elevation. Now look down onto the block, along the arrow marked 'plan" and draw what you see above the front elevation. This gives the plan and its exact position is determined by drawing lines from one of the end elevations at 45°.

Note that with 3rd angle protection, whet you see from the left you drew on the left, whet you see from the nght. you drew on the right, end whet you see from ebove you drew ebove

PLAN

/ Àà J

/ / ^-j a]

e&_| 1

¿it

1

ELEVATION ELEVATION (I)

Fig. 10/7 shows the same block drawn in 1st angle projection. Again, first draw the view obtained by looking along the arrow marked F.E. This gives the front elevation. Now look along the arrow marked E E., (which points from the left) and draw what you see to the right of the front elevation This gives you en end elevation. Now look along the arrow marked E. E 3 (which points from the right) and draw what you see to the left of the front elevation. This gives you another end elevation. Now look down on the block, elong the arrow marked plan' and draw what you see below the front elevation. This gives the plan and its exact position is determined by drawing lines from one of the end elevations at 45*.

ENO ELEVATION (2)

Fig. 10/8 3rd angle orthographic projection

Note that with 1st angle projection, whet you see from the left you drew on the right, whet you see from the right you drew on the left end whet you see from ebove you drew below.

Fig. 1Q/7 1st angle orthographic projection

...

-mLL?

Fig. 1Q/7 1st angle orthographic projection

Auxiliary elevations and auxiliary plana So far we have been able to draw four different views of the tame block. In moil engineering drawings these are sufficient but there are occasions when other views are necessary, perheps to clarify a particular point. Fig. 10/8 shows two examples where a view other than a F.E or an E.E. is needed to show very important features of e flanged p«pe and a bracket.

AUXILIARY PLAN 3RD ANGLE PROJECTION ¿^¡¡¿A** 'N

SHOWING FACE

DIRECTION OF ARROW

Fig. 10/8 These extra elevetions are called auxiliary elevations or auxiliary plans

Fig. 10/9 shows an auxiliary elevation (A.E.) and an auxiliary plan (A.P.) of the shaped block. One is projected from the plan at 30° and the other from the F.E. at 45® Projection linos are drawn at those angles and the heights, H and h. are marked off on one A.E- and the width W on the other. Remember that we are dealing with a solid block, not flat shapes on flat paper. Tiy to imagine the block as a solid object and these rather odd-shaped elevations will take on form and make sense

AUXILIARY PLAN 3RD ANGLE PROJECTION ¿^¡¡¿A** 'N

SHOWING FACE

DIRECTION OF ARROW

Fig. 10/8 These extra elevetions are called auxiliary elevations or auxiliary plans

Fig. 10/9 shows an auxiliary elevation (A.E.) and an auxiliary plan (A.P.) of the shaped block. One is projected from the plan at 30° and the other from the F.E. at 45® Projection linos are drawn at those angles and the heights, H and h. are marked off on one A.E- and the width W on the other. Remember that we are dealing with a solid block, not flat shapes on flat paper. Tiy to imagine the block as a solid object and these rather odd-shaped elevations will take on form and make sense

Fig 10/9

Fig 10/10 shows two auxiliary plans of a more complicated block. In this case the base is tilted and therefore cannot be used to measure the heights as before. This is overcome by drawing a datum line. The heights of all the comers are measured from this datum. Note that on the auxiliary plans the datum is drawn at 90® to the projection lines.

If the outline contain* circle* or curves, the treatment is similar. Select some points on the curve and mark off their distances from some convenient datum. In Fig. 10/11 this gives dimensions a. b. c. d. a and /. The positions of these points are marked on the plan end they are projected onto the A.E. The dimensions a to / are then marked off on the A.E. and the points joined together with a neat freehand curve.

It is worth stating again the difference between 1 st and 3rd angle projection, particularly if checked against the above examples With 1 st angle, if you look from one side of a view you draw what you see on the other side of that view. With 3rd angle, if you look from one side of a view you draw what you see on the same side of that view.

1ST ANGLE PROJECTION F£.

A£. SEEN IN DIRECTION OF ARROW

Fig 10/11

1ST ANGLE PROJECTION F£.

A£. SEEN IN DIRECTION OF ARROW

Shown below are some of the more common solid geometric solids drawn in orthographic projection.

Prisms and Pyremids

Fig 10/12 shows the following views of a rectangular prism, drawn in 1st angle projection with the pnsm tilted at 45" in the F E.

A F.E. looking along Arrow A. An E.E. looking along Arrow B. Apian.

An A.P. showing the cross-sectional shape of the prism.

1ST ANGLE PROJECTION

F. /

!

\

si

\

—

N

0

I

Fig. 10/13 shows the following views of a square pnsm drawn in 3rd angle projection The top 0f the pnsm has been cut obliquely at 30° A F.E. looking along Arrow A. An E.E. looking along Arrow B Apian

3R0 ANGLE PROJECTION

s

Fig. 10/14 shows the following views of a regular hexagonal pnsm. drawn in 3rd angle projection with the pnsm blted at 30° in the F.E The top of the prism has been cut obliquely at 45^.

A F.E. looking along Arrow A.

An E.E. looking along Arrow B.

Apian.

The first view that S drawn ts the A P This is not in the instructions but without it the F.E. is very difficult to draw Arrow A mdicatos that three sides of the hexagon are seen in the F.E. and the A P. is constructed so that three sides are seen (rotate the hexagon through 30* in the A.E and only two sides are seen) The A P. is also used to find the width of the pnsm in the E.E.

3R0 ANGLE PROJECTION

AP (Construction only)

Fig. 10/14 shows the following views of a regular hexagonal pnsm. drawn in 3rd angle projection with the pnsm blted at 30° in the F.E The top of the prism has been cut obliquely at 45^.

A F.E. looking along Arrow A.

An E.E. looking along Arrow B.

Apian.

3R0 ANGLE PROJECTION

Fig 10/14

1ST ANGLE PROJECTION F.E.

Fig. 10/15

Fig 10/15 show« the following views of the frustum of a square pyramid drawn in 1st angle projection. The comers of the pyramid are numbered 1 to 4 for easy identification on each elevation.

A F.E. looking along the arrow.

Apian.

1ST ANGLE PROJECTION F.E.

With this type of problem it is wise initially to draw the required views as if the pyramid were complete. Once again it is necessary to draw an A. E. so that the oblique face can be drawn on the A.E. and then points 1.2. 3 and 4 can be projected back onto the plan. Points 1 and 3 are then projected onto the F.E. and points 2 and 4 onto the

E.E. Points 2 end 4 can be projected from the E.E. to the

F.E. and points 1 and 3 from the F.E. to the E.E. Note that once the A.E. has been drawn It is possible to draw the oblique face on all three views without any further measuring

Fig. 10/15

Fig. 10/16 shows the following views of an octagonal pyramid drawn in 3rd angle projection. The pyramid is lying on its side.

A F.E. looking along the arrow.

Apian

To draw the pyramid lying on its side, first draw it standing upright and then tip it over. This is done with compasses as shown. If a plan of the pyramid standing upright is constructed, it makes it easier to find the positions of the corners of the pyramid in the plan when it has been lipped over.

3R0 ANGLE PROJECTION

3R0 ANGLE PROJECTION

Fig. 10/17 shows the following view* of a hexagonal pyramid drawn in 3rd angle protection. The top of the pyramid it cut et A& and the bottom at 30°.

A F.E. teen in the direction of the arrow.

A plan.

An A.E. projected from the plan at 3CP.

As for F»g. 10/15. the pyramid is first drawn as if it were complete, on all four views. The lower cutting plane is then drawn on the F.E. The points where it crosses the comers are then projected across to the E.E. and up to the plan The point where it crosses the centre comer on the F.E. cannot be projected straight to the plan and has to be projected via the E.E. (follow the arrows).

The upper cutting plane is then drawn on the E.E. and the points where it crosses the corners are projected across to the F.E. and up to the plan.

Most of these corners can be projected straight from the plan onto the A.E. The exceptions are the points on the centre corner and these (dimensions a. b. c and d) can be transferred from any convenient source, in this case the F.E.

Cylinder* end Cones

Fig. 10/18 shows the following views of a cylinder drawn in 1 st angle projection.

A F.E. seen in the direction of the arrow. Apian.

An AP projected from the F. E. at 46° If the plan is divided into a number of strips the width of the cylinder at any one of these strips can be measured. The exect positions of each of the strips can be projected onto the F.E. and then across to the A.P. The widths of the cylinder at each of the stnps is transferred from the plan onto the A P. with dividers, measured each side of the centre line (only one side is shown). The points are then joined together with a neat freehand curve.

1ST ANGLE PROJECTION

1ST ANGLE PROJECTION

Fig. 10/18

Fig 10/19 shows the following views of a cylinder drawn in 3rd angle projection The cylinder is lying on its side and one end is cut off ot 30® and the other end at 60" A F E. seen in the direction of the arrow. An E E. seen from the left of the F.E. Apian

An A. P. projectod from the plan at 60° The E.E. is divided into a number of strips The strips are projected from the E.E to the F.E. and up to the plan They are also projected from the E.E to the plan at 45? The points wheie the projector« from the F.E. and the E.E. meet on the plan (at a. b. c and d. etc) give the outline of the two ellipses on the plan.

The outline of the ellipses on the A P are found by projecting the strips onto the A P. and then transferring measurements 1, 2, 3. etc from the E.E. to the AP with dividers.

This drawing use« a different method of plotting an A.P. from the previous two examples Instead of being divided into »trips, the cylinder is divided into 12 equel segments Thesa are marked on the walls of the cylinder as numbers, from 1 to 12. The ellipses formed on the A.P. are found by plotting the intersections of the projectors of numbers 1 to 12 from the F.E. and from a construction drawn in line with the A.P. The projectors intersect in 1', 2'. 3* etc. Note that on the E.E. number 1 is at the top of the circle whilst on the construction (and hence on the A.P.) number 1 is on the right. This, of course, is what you should expect

1ST ANGLE PROJECTION

(Construction only)

Fig. 10/20

1ST ANGLE PROJECTION

(Construction only)

Fig. 10/20

Fig. 10/21 shows the following views of a cylinder drawn in 3rd angle projection. The base of the cylinder is cut obliquely at 30* and the cylinder is tilted at 60» in the F.E.

A F.E. seen in the direction of the arrow. An E.E. seen from the left of the F.E.

Apian. 3RD ANGLE PROJECTION

PLAN

The cylinder is divided into twelve equal segments. This is done on a separate auxiliary elevation and plan which are constructed just for that purpose The ellipses are found by plotting the intersections o< the projectors from points 1 and 1.2 and 2,3 and 3. 4 and 4. etc.

PLAN

(Construction only)

Fig. 10/21

(Construction only)

Fig. 10/21

r (Construelion only)

1ST ANGLE PROJECTION

1ST ANGLE PROJECTION

Fig. 10/22 shows the following views of a cone drawn in 1 st angle projection.

A F.E. seen in the direction of the arrow

Apian

The plan is divided into strips. These strips ere projected across to the E.E. and hence to the A.P. The width of the base of the cone on esch of these strips is measured on the plan with dividers and transferred onto the A P. The points are then joined with a neat freehand curve.

SChl

Fig. 10/23 shows the following views of a cone drawn in 3rd angle projection. The cone is lying on its side.

A F.E. seen in the direction of the arrow.

Apian

The cone is first drawn standing upnght and it is then tipped over to lie on its side Instead of being divided into strips as before, it is divided into 12 equal segments. These are numbered from 1 to 12 on two constructions drawn in line with the F.E. and the E E. The ellipses formed on the E.E. and the plan are found by plotting the intersections of the projectors from these constructions. They intersect in 12*. 3\ etc on the E.E. and on the plan.

The geometry of cones is explored much more fully In the next chapter.

Sections

Suppose that you make a drawing of a box. You draw the box in orthographic projection end ere pleased with the result. But someone comes along and says, quite reasonably. It's a good drawing but after ell. a box is only a container and you haven't shown what is inside the box; surely thet is whet is importent". And of course, he is right It is often vital to show what is inside an object as well as to show the outside. In orthographic projection, this is catered for with e section.

3RD ANGLE PROJECTION PLAN_

3RD ANGLE PROJECTION PLAN_

Fig. 10/24 shows two drawing» of the aame block, one drawn without i section and on« drawn with a section. Tha upper drawing does not show clearly on any one of the orthographic views that the block is hollow. On the lower left isometric view, the block has been cut in hetf and it is immediately obvious that ths block rs hollow. Tha lower right view shows the cut block drawn in orthographic projection. Again, it is much eesier to see that the block Is hollow.

Note carefully the following ml es:

1. The sectioned E.E. is drawn with half of the block missing but non» of th» other views ere effected. They keep their normal full outline.

2. The point where tha section is made is denoted by a cutting plane. This is drawn with a thin chain dot line which is thickened where it changes direction and for a short distance at the end. The arrows point in the direction that the section is projected.

3. Where the cutting plane cuts through solid material, the material is hatched at 45*.

4. When a section is projected, the remaining visible features which can be seen on the other side of tha cutting plane are also drawn on the section.

6. It is not usual to draw hidden deuil on a section.

There are many rules about sectioning but most of them apply to engineering drawing, rather than geometric drawing. For this reason they are found in the second

3RD ANGLE PROJECTION

1ST ANGLE PROJECTION

Fig. 10/26

Fig 10/25

Fig 10/25 «hows a section taken from a hexagonal

This type of problem contains all the characteristics of auxiliary elevations and the same methods are used to project this section.

Sometimes questions set in examination papers do not ask specifically for a section but the same methods have to be used to find the solution.

Fig. 10/26

Fig. 10/26 shows a cream jug which is shaped in the form of the frustum of a hexagonal pyramid The problem is to find the true shape of the lid.

The solution is to project a 'section' (or an A E.) from the oblique top of the pyramid First draw the F.E.. then the plan. The true widths a and b can be measured on the plan and these measurements transferred to the 'section' with dividers.

Fig. 10/27 »how« a taction projected from a piece of thick wall tubing that is attached to a rectangular base Apart from the F.E. a plan must be drawn. Points around the circumference of the circles on the pUn are selected and these points are projected down to the section plane and then across onto the section itself. The centre line is a convenient datum and so the distance from each point to the centre line is measured with dividers and transferred to its corresponding projection line on the section. For clarity, only seven points are shown but. of course, all the points round the circumference would have to be measured end transferred.

There are two points to note from this drewtng. Firstly, the section hatching is not drawn at 45*. This is because the hatching would then be parallel to a large part of the outline. In this type of case, an angle other than 45* can be adopted Secondly, note that hatching is done only where the section (or cutting) plane actually cuts through solid material.

3RD ANGLE PROJECTION

3RD ANGLE PROJECTION

Finally. Fig 10/28 shows a section through a socket spanner. One end hat a hexagonal recess to fit a nut or bolt head and the other has a square recess to accom modate a tommy bar. The circular profile is again split up so that points along its circumference can be measured and the measurements transferred onto the section via the section plane. The points where the section plana crosses the hexagonal and squaie sockets are projected onto the section and any measurements that have to be made are found by projecting back to one of the end elevations. These are marked a. b. c and d The measurements for the outside profile are marked (rom t to 8

For clarity only half of the measurements are shown. The other half is dealt with in the seme way. Conic sections are dealt with in the next chapter Sections applied to engineering drawings are dealt with in Pan 2 of this book.

Fig. 10/28

Exercises 10 (All questions onginalfy set in Impehel units)

1. Fig. 1. shows the elevation of a 20 mm square prism 50 mm long resting with one of its corners on the horizontal plane Draw, full size, the following views and show all the hidden detail.

(a) The given elevation

(b) An end elevation looking in the direction of arrow E.

(c) A plan projected beneath view (a).

North Waste/n Secondary School Examinations Board

2. Fig. 2 shows the front elevation and an isometric sketch of a sheet metal footiight reflector for a puppet

Fig. 10/28

Draw, full site, the given front elevation and from it project the plen and end view of the reflector Draw. also, the true shape of the surface marked ABCO.

The thickness of the metal can be ignored Wast Midlands Examinations Board

Fig 2

Fig 2

14. The plan and elevation of a special angle bracket are shown in Fig. 14.

(a) Draw, full-size, the given views and project an auxiliary plan on the ground line X,-Y,.

(b) Using the auxiliary plan in (a) above, project an auxiliary elevation on the ground line X,-Yt.

15. Two views of a pivot block ere shown in Fig 15. Draw the given views, snd produce an elevation on XY as seen when looking in the direction of arrow A. Hidden edges are to be shown. Cambridge Local Examinations

DIMENSIONS IN mm Fig. 16

DIMENSIONS IN mm Fig. 16

17. Fig. 17 shows an elevation and a plan of a casting of a corner cremp in which the shape is symmetrical about AA.

Draw a second elevation looking in the direction of arrow B.

Draw a sectional elevation on the cutting plane AA. Hidden detail is required on all views. Southern Universities' Joint Board